A concert starts in seventeen minutes and four guys must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses (either one or two people) must have the flashlight with them. The flashlight must be walked back and forth. It cannot be thrown etc. Each person walks at a different speed. A pair must walk together at the rate of the slower man's pace.

Bandmate	Time to cross
Bono	1 minute
Edge	2 minutes
Adam	5 minutes
Larry	10 minutes

For example, if Bono and Larry walk across first, ten minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of twenty minutes have passed and you have failed the mission. Note: there are two known answers to this problem.

This problem has circulated for some time. We first heard of it from Van Ma at Nicholls State University about a year before this submission.

Hint 1

This kind of problem is worked by trial and error, so the intellectual challenge is to think of ways to cut down the number of trials. Try this: without worrying about who goes when, think about the number of trips that might be needed and what the time of each trip might be. For example, any trip including Larry is a 10-minute trip, so there is at least one 10-minute trip.

Hint 2

One way to cut down the number of trials is to make some plausible assumptions.

Let's assume the solution requires exactly 17 minutes (the problem only asks for 17 minutes or less, but "problem psychology" tells us that if it could have been done in 16 minutes, they would have asked for 16 minutes).
There have to be at least 5 trips, because each round trip across the bridge and back can only increase the number of persons on the far side by 1 (the trip across can increase it by 2, but then 1 has to come back). So after 2 round trips we have at most 2 people on the far side, and the remaining 2 could come on the next one-way trip, for a total of 5 trips. So let's assume the solution can be done in exactly 5 trips.

The possible trip times are 1, 2, 5, and 10 minutes. What are some feasible combinations of 5 numbers, taken from these four (with repetitions allowed), that add up to 17?

Click here if you need another hint.

Click here for the solution.